MaximeRey Algebraicconstructionsonsetpartitions

After reviewing the definition of the restricted quantum group U q sℓ(2), we give our quasi-Hopf algebra modification U (Φ) q sℓ(2), and we show that it is indeed a factorisable

The study of this dendriform structure is postponed to the appendix, as well as the enumeration of partitioned trees; we also prove that free Com-Prelie algebras are free as

As explained in [8], the space generated by the double posets inherits two products and one coproduct, here denoted by m, and ∆, making it both a Hopf and an infinitesimal Hopf

The Connes-Kreimer Hopf algebra of rooted trees, introduced in [1, 6, 7, 8], is a commutative, non cocommutative Hopf algebra, its coproduct being given by admissible cuts of trees2.

The main point of the construction is a Hopf algebra morphism Θ from H o to the Hopf algebra of free quasi-symmetric functions FQSym [4, 17], also known as the Malvenuto-Reutenauer

A non-degenerate pairing and a dual basis are defined, and a combinatorial interpretation of the pairing in terms of orders on the vertices of planar forests is given.. Moreover,

Free quasi- symmetric functions, product actions and quantum field theory of partitions.... Duchamp † , Jean-Gabriel Luque ‡ , K A Penson ⋆ Christophe Tollu † , ( † ) LIPN, UMR

The classes of (labelled) diagrams up to this equivalence (permutations of white - or black - spots among themselves) are naturally represented by unlabelled diagrams and will